Abstract : A new approach to the interpretation of the vibrational spectra of high polymers is presented. An attempt was made to develop a new mathematical technique for the predictions of the spectroscopic behavior of polymers containing a random distribution of mass defects. Polyethylene and its deuteroderivatives were studied. The spectra of several copolymers of different isotopic derivatives of ethylene were predicted and compared with the experimental data. The cis opening of the double bond of ethylene during the polymerisation reaction has been again unequivocally confirmed. A preliminary calculation on the spectrum of poly-(vinyl chloride) containing a random distribution of conformational and configurational defects is presented and compared with the experimental findings. A generalisation is presented of the well known GF method for normal coordinate calculations which can be applied for the calculation of normal vibrations of crystals in three dimensions. A hermitian dynamical matrix in terms of cartesian displacement coordinates is derived starting from a harmonic force constants matrix expressed in terms of the Wilson's internal displacement coordinates.